Question

A) using the product rule, not the chain rule, show that d/dx [f(x)]^2 = 2f(x) f ' (x).

 

B) let f(x) and g(x) be functions and le p(x)=f(x) g(x) and q(x) = f(x)/g(x) be their proodduct and quotient, respectively. use the following information to determine p'(3) aand q'(3).

f(3)=-2, f'(3)=3  g(3)=7, g'(3)=4

Answer 1

A)

Apply derivative with respect of x .

Apply product rule in derivatives.

In this case

Answer 2

B) f (3) = - 2, f '(3) = 3, g (3) = 7 and g '(3) = 4.

• The function

Apply derivative on each side with respect of x .

Apply product rule in derivatives.

• The function

Apply derive on each side with respect of x .

Apply quotient rule in derivatives.